Convergence and quasi-optimality of adaptive finite element methods for harmonic forms
Sign Up to like & getrecommendations! Published in 2017 at "Numerische Mathematik"
DOI: 10.1007/s00211-016-0862-6
Abstract: Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework also relies extensively on accurate computation… read more here.
Keywords: finite element; adaptive finite; element methods; harmonic forms ... See more keywords
Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation
Sign Up to like & getrecommendations! Published in 2022 at "Numerische Mathematik"
DOI: 10.1007/s00211-021-01259-8
Abstract: Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices have to be computed… read more here.
Keywords: boundary element; wave equation; cross approximation; approximation ... See more keywords
Expandable Parallel Finite Element Methods for Linear Elliptic Problems
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DOI: 10.1007/s10473-020-0218-2
Abstract: In this article, two kinds of expandable parallel finite element methods, based on two-grid discretizations, are given to solve the linear elliptic problems. Compared with the classical local and parallel finite element methods, there are… read more here.
Keywords: finite element; linear elliptic; parallel finite; expandable parallel ... See more keywords
Finite Element Methods for a System of Dispersive Equations
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DOI: 10.1007/s10915-018-0767-x
Abstract: The present study is concerned with the numerical approximation of periodic solutions of systems of Korteweg–de Vries type, coupled through their nonlinear terms. We construct, analyze and numerically validate two types of schemes that differ… read more here.
Keywords: finite element; system; dispersive equations; methods system ... See more keywords
Hybridization and stabilization for hp-finite element methods
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DOI: 10.1016/j.apnum.2018.09.017
Abstract: Abstract In this paper various hybrid hp-finite element methods are discussed for elliptic model problems. In particular, a stabilized primal-hybrid hp-method is introduced which approximatively ensures continuity conditions across element interfaces and avoids the enrichment… read more here.
Keywords: stabilized primal; hybrid method; element methods; primal hybrid ... See more keywords
Numerical Analysis of Fully discrete Finite element Methods for the stochastic Navier-Stokes Equations with Multiplicative Noise
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DOI: 10.1016/j.apnum.2021.07.018
Abstract: Abstract Previous work on the stability and convergence analysis of the finite element methods for the deterministic Navier-Stokes equations was carried out under the uniqueness condition. In this paper, the corresponding results of fully discrete… read more here.
Keywords: stokes equations; element methods; fully discrete; finite element ... See more keywords
Compatible-strain mixed finite element methods for 2D compressible nonlinear elasticity
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DOI: 10.1016/j.cma.2016.09.047
Abstract: Abstract In this paper, using the Hilbert complexes of nonlinear elasticity, the approximation theory for Hilbert complexes, and the finite element exterior calculus, we introduce a new class of mixed finite element methods for 2D… read more here.
Keywords: finite element; mixed finite; nonlinear elasticity; element methods ... See more keywords
Interface-penalty finite element methods for interface problems in H1, H(curl), and H(div)
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DOI: 10.1016/j.cma.2020.113137
Abstract: Abstract In this article, interface-penalty finite element methods are proposed to solve interface problems in H 1 , H ( curl ) , H ( div ) spaces on unfitted tetrahedral meshes. The transmission conditions… read more here.
Keywords: interface penalty; finite element; element methods; interface ... See more keywords
Computation of electric field inside substations with boundary element methods and adaptive cross approximation
Sign Up to like & getrecommendations! Published in 2018 at "Engineering Analysis With Boundary Elements"
DOI: 10.1016/j.enganabound.2018.03.002
Abstract: Abstract Power system substations and HV power lines are sources of electric and magnetic fields of industrial frequency. Guidelines for permissible electric and magnetic field strengths regarding human exposure and electromagnetic compatibility (EMC) are provided… read more here.
Keywords: computation; field; element methods; adaptive cross ... See more keywords
Fully Discrete Interpolation Coefficients Mixed Finite Element Methods for Semi-Linear Parabolic Optimal Control Problem
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DOI: 10.1109/access.2022.3173402
Abstract: We use the fully discrete interpolation coefficient mixed finite element methods to solve the semi-linear parabolic optimal control problems. The space discretization of the state variable is separated using interpolation coefficient mixed finite elements. We… read more here.
Keywords: control; finite element; mixed finite; interpolation ... See more keywords
Variational Multiscale Finite-Element Methods for a Nonlinear Convection–Diffusion–Reaction Equation
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Applied Mechanics and Technical Physics"
DOI: 10.1134/s0021894420070226
Abstract: This paper is devoted to developing finite-element methods for solving a two-dimensional boundary value problem for a singularly perturbed time-dependent convection–diffusion–reaction equation. The solution to this problem may vary rapidly in thin layers. As a… read more here.
Keywords: element methods; problem; finite element; diffusion ... See more keywords